Simplify to lowest terms. $\dfrac{36}{54}$
There are several ways to tackle this problem. What is the greatest common factor (GCD) of 36 and 54? $36 = 2\cdot2\cdot3\cdot3$ $54 = 2\cdot3\cdot3\cdot3$ $\mbox{GCD}(36, 54) = 2\cdot3\cdot3 = 18$ $\dfrac{36}{54} = \dfrac{2 \cdot 18}{ 3\cdot 18}$ $\hphantom{\dfrac{36}{54}} = \dfrac{2}{3} \cdot \dfrac{18}{18}$ $\hphantom{\dfrac{36}{54}} = \dfrac{2}{3} \cdot 1$ $\hphantom{\dfrac{36}{54}} = \dfrac{2}{3}$ You can also solve this problem by repeatedly breaking the numerator and denominator into common factors. For example: $\dfrac{36}{54}= \dfrac{2\cdot18}{2\cdot27}= \dfrac{2\cdot 3\cdot6}{2\cdot 3\cdot9}= \dfrac{2\cdot 3\cdot 3\cdot2}{2\cdot 3\cdot 3\cdot3}= \dfrac{2}{3}$